many websites in Japan has two name field: one is kanji, another is katakana.
https://shinkabukiza.pia.jp/membmng/RegisterNormalAction.do
Take this for example, the field in first row is full-width kanji, second one is full-width katakana.
The フリガナ (furigana) field is to indicate how the name given above is read, because kanji can have many readings including completely arbitrary ones. This also serves to indicate how computers should index and sort the names when storing and processing them, so it's still applicable even if the name is all hiragana or katakana and immediately obvious.
Furigana is also used to indicate how to read kanji in ordinary text, oftentimes when dealing with rare kanji or special readings, when the text must be comprehensible by everyone (eg: emergency bulletins), or when the text is written for people learning Japanese (eg: school textbooks).
Furigana is usually written using hiragana, so the reason 全角カタカナ (full width katakana) is specified instead of just full width is to inform the form's filer that he shouldn't write hiragana like he otherwise probably would.
https://en.wikipedia.org/wiki/J%C5%8Dy%C5%8D_kanji
Is it common to come across names using kanji outside that range?
Even in English this happens, look at all the variations of Robert (Rob, Bob, Robb, Robbie, Bobbie, ...) or similar names.
That doesn't quite grasp the magnitude. We're talking on the level of writing "Charlie" and reading it as "Alexander". Why? Because yes, that's why.
Providing readings using furigana is the mechanical answer to a very human problem.
I'm thinking.. I've only ever seen someone's name, will I make serious faux pas if I mispronounce it with the regular reading when I meet them?
(this is less pronounced in English because most of the time you can tell how to pronounce it by reading it. My last name suffers from the fact there is multiple possible pronunciations, so whenever I meet someone who has never heard my name they always stumble and look at me for help)
As for business cards, yes, if they have some non-obvious reading they will have kana or romaji there somewhere. (Usage of romaji on business cards is wider than you might expect, since it's seen as kind of the equivalent of a modern sans-serif logo for a business in some circles)
e.g.
Card with furigana: https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...
Card with kana elsewhere: https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...
Card with romaji: https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...
On the first example -- what is the significance of the character which is a circle within a circle? I'm assuming it's some sort of graphic or punctuation, rather than a kanji...?
The heading of that corner is just the pronounication of "m-take design" written out in katakana. The first line under the heading talks about the type of products the person works on (direct mail, leaflets, pamphlets). The second line talks about their specialities, as in the industries they focus on (cosmetics, health food), and then the last mentions they'll also do logo design, homepage design etc. I guess they wanted to emphasize the second line.
You'll sometimes see kanji-sized single circles used in Japan to indicate omitted characters (and you might see them on business card _templates_ as a sort of lorem ipsum, but unlikely on actual business cards), but this double circle doesn't have any specific meaning as far as I know.